Transparent background for live motion capture and performance
The easiest method for me would be using green background in Blender and Chroma key filter in OBS Studio:


In Blender, set Display -> Render Only and tick World Background


Set World Background Color to green


Hide all UI so it looks like this, you can go fullscreen by pressing AltF11

In OBS Studio, add corresponding Display or Window to Sources list, then right click on the scene preview -> Filters -> Chroma Key, make sure the green is selected

The resulted scene you can live stream